四元数代数与群环的序的双曲性
环与代数
2007-05-23 v2 群论
摘要
对于给定的四元数除代数，我们构造两类单位：佩尔单位与高斯单位。若 K 为有理二次扩张、G 为有限群，我们分类 R 与 G，使得增广为 1 的 unit group U(RG) 是双曲的。特别地，我们给出当 G 为 8 阶四元数群时的充要条件。在此情形下，双曲边界同构于 2 维球面。作为结果，我们得到一类单端且非 virtually free 的群。
引用
@article{arxiv.math/0610699,
title = {Hyperbolicity of Orders of Quaternions Algebras and Group Rings},
author = {S. O. Juriaans A. C. Souza Filho},
journal= {arXiv preprint arXiv:math/0610699},
year = {2007}
}
备注
This report is part of the first chapter of the second author's PhD. Thesis. It was included a result in main theorem and a sketch of its proof before it, as well as two new references